Cook County Sheriff Tom Dart says he wants changes to an ordinance that frees some jail inmates wanted by immigration authorities. But the law’s supporters say they still have the votes to keep it intact.

The ordinance, approved last September, prohibits the sheriff from complying with U.S. Immigration and Customs Enforcement detainers. Those are requests that the county hold specified inmates up to two business days longer than their criminal cases require. The detainers gave ICE extra time to pick up the inmates for possible deportation.

The ordinance has come under fire as news outlets have focused on a convicted felon who completed his probation before going to jail on charges of killing a man in a Northwest Side hit-and-run incident last year. ICE named the inmate on a detainer. After the ordinance passed, he posted bond, walked free and went missing.

On Thursday, a County Board committee held a four-hour hearing on proposals to honor the detainers for inmates who are potentially dangerous. At the hearing, Dart said the jail had released 346 inmates named on ICE detainers since the ordinance passed. He said 11 of those ended up arrested again on a variety of charges.

Dart also voiced support for one of those proposals, an amendment introduced last month by Timothy Schneider (R-Bartlett) that would require compliance with the detainers for inmates who appeared on a federal terrorist list or who faced various felony charges. Dart said Schneider’s proposal would target inmates who “have shown that they’re a danger.” Dart criticized another proposal, an amendment filed by Peter Silvestri (R-Elmwood Park) and John Daley (D-Chicago), that would give the sheriff discretion to honor detainers.

Commissioner Larry Suffredin (D-Evanston), who chairs the committee, told WBEZ he opposes both amendments and said neither has enough support to pass. But Suffredin, who voted for the ordinance, said he is open to “cleaning it up to give the sheriff clearer discretion” on whether to honor detainers. Suffredin said any committee votes on amending the ordinance would be next month.

County Board President Toni Preckwinkle, interviewed by WBEZ during the hearing, pointed out that many citizens get out of jail and cause trouble, too.

“People who are accused of very serious crimes are given bail every day because a judge makes a determination that they’re not a flight risk and they’re not a danger to our community,” she said. “So if you have a concern about people who are accused of serious crimes being released back into our community, it’s got to be broader concern than the two or three percent of them who are undocumented.”

Preckwinkle talked up a study that’s looking for ways to improve the bond system. The county’s five-member Judicial Advisory Council is carrying out the study and planning to make recommendations within six months.

The ordinance, sponsored by Commissioner Jesús García (D-Chicago), prohibits the jail from honoring the detainers unless the federal government agrees in advance to pay for the extended confinement — something ICE says it doesn’t do. The law’s supporters say the detainers eroded community trust in local police and violated inmates’ due-process rights. A federal court ruling in Indiana last summer called compliance with the detainers “voluntary.”